There are some exceptions. Most white Southerners are descended from 17th and 18th Century settlers from the British Isles. There are portions of the Upper Midwest that are still basically German, Dutch, or Scandinavian. A few ethnic neighborhoods still hang on in the Northeastern and Great Lakes cities, although the vast majority of the "Ellis Island" immigrants have long since migrated to suburbia or the Sun Belt.
There is nothing different in the development of a common white or Euro-American identity than what Hispanics, Asians, American Indians, and blacks have done in bridging their internal differences to forge a common identity. However, in the Orwellian world of liberalism, whites are not permitted the same liberty that non-whites have in these matters.
BTW: I don't buy the idea of "Hispanics" forging a single identity. Granted, if you are a meztizo from Guatemala living surrounded by meztizos from Mexico, you will assimilate into that culture. Nevertheless, try telling a (usually white) Cuban that he/she is the same culture as some Chicano in California and they will go berserk (as they should).
My husband was full-blooded Czech, and he was born here, as were his parents, and his grandparents on both sides imigrated with their parents as children. There are no racial lines crossed in his family until this most recent generation (Those born after 1995). 95% of the grandchildren of his parents are pure-blooded Czech, the rest are 50%. The last of the full-blooded turn of the (20th) Century immigrants from Central Europe are dying out, and very few of their descendants will be full-blooded. In one way, it's sad to see, but as Americans first, perhaps the melting-pot idea is the best.
I don't know...I'm just a British mutt (Scots, Irish, English, and Welsh).